Change start time for each camera
Use Multicam Selector Effect in VSE


Add Scene strip
Make as many copies as your cameras (Shift + D + Y + move the strip to a different channel)
Assign a different camera to every Scene strip in the Properties Panel (N)





Add a Multicam Selector Effect and assign the channel of the desired strip

You can either add multiple Multicam Selector Effects, or cut one Strip by placing the cursor at the right frame and pressing a "Cut to" button (1, 2...) 









Check Sequencer in the render Panel